{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-09-11T03:39:09.054034Z",
     "start_time": "2025-09-11T03:39:08.801779Z"
    }
   },
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "# 设置中文字体支持\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei', 'DejaVu Sans']  # 用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus'] = False  # 用来正常显示负号\n",
    "\n",
    "# 设置随机种子以确保结果可重现\n",
    "torch.manual_seed(42)\n",
    "np.random.seed(42)\n",
    "\n",
    "# 1. 生成数据\n",
    "a_true = 2.5  # 真实斜率\n",
    "b_true = 1.3  # 真实截距\n",
    "num_points = 100  # 数据点数量\n",
    "\n",
    "# 生成x值\n",
    "x = torch.linspace(0, 10, num_points).unsqueeze(1)\n",
    "\n",
    "# 生成y值并添加噪声\n",
    "y_true = a_true * x + b_true\n",
    "noise = torch.randn(x.size()) * 2.0  # 标准差为2的正态分布噪声\n",
    "y = y_true + noise\n",
    "\n",
    "\n",
    "# 3. 使用PyTorch进行梯度下降\n",
    "# 定义模型参数（初始化为随机值）\n",
    "a = torch.randn(1, requires_grad=True)\n",
    "b = torch.randn(1, requires_grad=True)\n",
    "\n",
    "# 定义学习率和迭代次数\n",
    "learning_rate = 0.01\n",
    "num_epochs = 1000\n",
    "\n",
    "# 存储损失值\n",
    "losses = []\n",
    "\n",
    "# 梯度下降循环\n",
    "for epoch in range(num_epochs):\n",
    "    # 前向传播：计算预测值\n",
    "    y_pred = a * x + b\n",
    "\n",
    "    # 计算损失（均方误差）\n",
    "    loss = torch.mean((y_pred - y) ** 2)\n",
    "    losses.append(loss.item())\n",
    "\n",
    "    # 反向传播：计算梯度\n",
    "    loss.backward()\n",
    "\n",
    "    # 更新参数（不追踪梯度）\n",
    "    with torch.no_grad():\n",
    "        a -= learning_rate * a.grad\n",
    "        b -= learning_rate * b.grad\n",
    "\n",
    "        # 清零梯度\n",
    "        a.grad.zero_()\n",
    "        b.grad.zero_()\n",
    "\n",
    "    # 每100轮打印一次损失\n",
    "    if (epoch + 1) % 100 == 0:\n",
    "        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')\n",
    "\n",
    "# 4. 绘制损失曲线\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(range(num_epochs), losses)\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss (MSE)')\n",
    "plt.title('Training Loss')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# 5. 绘制最终拟合结果\n",
    "y_fit = a.detach() * x + b.detach()\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(x.numpy(), y.numpy(), alpha=0.7, label='Data with noise')\n",
    "plt.plot(x.numpy(), y_true.numpy(), 'r-', linewidth=2, label='True linear relationship')\n",
    "plt.plot(x.numpy(), y_fit.numpy(), 'g--', linewidth=2, label='Fitted result')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Fitting Result Comparison')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# 6. 比较参数差距\n",
    "a_final = a.item()\n",
    "b_final = b.item()\n",
    "\n",
    "print(f\"\\nParameter comparison:\")\n",
    "print(f\"True parameters: a = {a_true:.4f}, b = {b_true:.4f}\")\n",
    "print(f\"Fitted parameters: a = {a_final:.4f}, b = {b_final:.4f}\")\n",
    "print(f\"Parameter differences: Δa = {abs(a_final - a_true):.4f}, Δb = {abs(b_final - b_true):.4f}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [100/1000], Loss: 4.0806\n",
      "Epoch [200/1000], Loss: 3.9363\n",
      "Epoch [300/1000], Loss: 3.8829\n",
      "Epoch [400/1000], Loss: 3.8632\n",
      "Epoch [500/1000], Loss: 3.8559\n",
      "Epoch [600/1000], Loss: 3.8532\n",
      "Epoch [700/1000], Loss: 3.8522\n",
      "Epoch [800/1000], Loss: 3.8518\n",
      "Epoch [900/1000], Loss: 3.8517\n",
      "Epoch [1000/1000], Loss: 3.8516\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Parameter comparison:\n",
      "True parameters: a = 2.5000, b = 1.3000\n",
      "Fitted parameters: a = 2.4898, b = 1.4678\n",
      "Parameter differences: Δa = 0.0102, Δb = 0.1678\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "224669bf8aae37a0"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
